A doughnut shop at a shopping mall sells a dozen doughnuts for $2.95. Beyond the fixed costs of $150 per day, it costs $1.45 for enough materials and labor to produce each dozen doughnuts. If the daily profit varies between $50 and $200, between what levels (in dozens) do the daily sales vary?
For each dozen sold, the unit profit is $2.95-$1.45=$1.50.
If the net profit (after overhead and cost) is $50 per day, the number of dozens sold is ($150+$50)/1.50=400/3 dozens.
If the net profit is $200, the number of dozens sold is ($150+$200)/1.5=700/3 dozens.
Thus, the daily sales vary from 133.3 dz to 233.3 dz., approximately.
To determine the range of daily sales in dozens, we need to consider the profit made per dozen doughnuts and the daily profit.
Let's start by calculating the profit made per dozen doughnuts:
Profit per dozen doughnuts = Selling price per dozen - Cost per dozen
Profit per dozen doughnuts = $2.95 - $1.45
Profit per dozen doughnuts = $1.50
Next, we need to determine the number of dozens sold per day to achieve the given profit range. We can do this by dividing the daily profit by the profit made per dozen doughnuts.
For the lower range of $50:
Number of dozens sold = Daily profit / Profit per dozen doughnuts
Number of dozens sold = $50 / $1.50
Number of dozens sold = 33.333 (approximately)
Since we cannot sell a fraction of a dozen, we round up to the next whole number.
Number of dozens sold in lower range = 34 dozens
Similarly, for the upper range of $200:
Number of dozens sold = $200 / $1.50
Number of dozens sold = 133.333 (approximately)
Again, we round up to the next whole number.
Number of dozens sold in upper range = 134 dozens
Thus, the daily sales vary between 34 dozens and 134 dozens.